- Email: [email protected]

ScienceDirect

IFAC PapersOnLine 51-31 (2018) 262–267

Active Thermal Control of a Battery Active Thermal Control of a Battery ActiveUnder Thermal Control of a Battery⋆⋆ Elevated Temperatures ActiveUnder Thermal Control of a Battery Elevated Temperatures Under Elevated Temperatures ⋆⋆ Under Elevated Temperatures ∗,∗∗ ∗,∗∗ Xiaojing Gao ∗∗ ∗∗ Yan Ma ∗,∗∗ Hong Chen ∗,∗∗

Pack Pack Pack Pack

Xiaojing Gao ∗∗ Yan Ma ∗,∗∗ Hong Chen ∗,∗∗ Xiaojing Gao ∗∗ Yan Ma ∗,∗∗ Hong Chen ∗,∗∗ ∗∗ ∗,∗∗ ∗,∗∗ Xiaojing Gao Yan Ma Hong Chen ∗ Key Laboratory of Automotive Simulation and Control, Jilin ∗ State State Key Laboratory of Automotive Simulation and Control, ∗ State Key Laboratory of Automotive Simulation and Control, Jilin Jilin University, Changchun, China. (e-mail: mayan [email protected]) ∗ University, Changchun, China. (e-mail: mayan [email protected]) State Key Laboratory of China. Automotive Simulation and Control, Jilin University, Changchun, (e-mail: mayan [email protected]) (e-mail: [email protected]). (e-mail: [email protected]). ∗∗University, Changchun, China. (e-mail: mayan [email protected]) (e-mail: [email protected]). Science and ∗∗ Department of Control Department of Control Science and Engineering, Engineering, Jilin Jilin University, University, ∗∗ (e-mail: [email protected]). Department of Control Science and Engineering, Jilin University, Changchun, China.([email protected]). ∗∗ Changchun, China.([email protected]). Department of Control Science and Engineering, Jilin University, Changchun, China.([email protected]). Changchun, China.([email protected]). Abstract: This This work work studies studies the the battery battery thermal thermal management management employing employing fuzzy fuzzy logic logic control control Abstract: Abstract: This work studies the battery thermal model management employing fuzzy logic control (FLC). This work ﬁrst develops the reduced-order (ROM) of a battery pack whose heat (FLC). ThisThis workwork ﬁrst studies developsthe thebattery reduced-order model (ROM) employing of a battery packlogic whose heat Abstract: thermal management fuzzy control (FLC). This work ﬁrst develops the reduced-order model (ROM) of a battery pack whose heat transfer coeﬃcient varies with coolant ﬂow velocity. Then, the ROM is simpliﬁed to obtain transfer coeﬃcient varies with coolant ﬂow velocity. Then, the ROM is simpliﬁed to obtain (FLC). This workrange ﬁrst develops the reduced-order model (ROM) of a battery pack whose heat transfer coeﬃcient varies with coolant ﬂow velocity. Then, ROM is(CFD) simpliﬁed to isobtain the temperature temperature of battery battery pack. A computational ﬂuidthe dynamics model built the range of pack. A computational ﬂuid dynamics (CFD) model isobtain built transfer coeﬃcient varies with coolant ﬂow velocity. Then, the ROM is simpliﬁed to the battery pack.ofAROM. computational ﬂuid dynamics (CFD) model is built and temperature validated to to range verifyofthe the accuracy Finally, based based on the the ROM, ROM, diﬀerent control and validated verify accuracy ofAROM. Finally, on diﬀerent control the temperature of battery pack. computational ﬂuid dynamics (CFD) model is built and validated to range verify the accuracy of ROM. Finally, based on ANSYS the ROM, diﬀerent control strategies are used to control the temperature of battery pack. and MATLAB costrategies are used to control the temperature of battery pack. ANSYS anddiﬀerent MATLAB coand validated to verify the accuracy of ROM. Finally, based on the ROM, control strategies are used to to control thethe temperature ofofbattery pack. ANSYS and MATLAB cosimulation is proposed validate eﬀectiveness FLC. The simulation results suggest that simulation is proposed to validate the eﬀectiveness of FLC. The simulation results suggest that strategies are used control thethe temperature ofof battery pack. ANSYS results and MATLAB cosimulation is proposed to validate eﬀectiveness FLC. The simulation suggestvalue, that FLC, compared compared withtoPID PID control, rapidly controls the battery temperature in expected expected FLC, with control, rapidly controls the battery temperature in value, ◦ of simulation is proposed to validate the eﬀectiveness FLC. The simulation results suggest that FLC, compared with PID control, rapidly controls the battery temperature in expected value, and ensures ensures temperature temperature control control error error within within 0.2 0.2 ◦ C. and C. FLC, compared with PIDcontrol control,error rapidly controls the battery temperature in expected value, and ensures temperature within 0.2 ◦◦ C. © 2018, IFACtemperature (Internationalcontrol Federation of Automatic and ensures error within 0.2Control) C. Hosting by Elsevier Ltd. All rights reserved. Keywords: Battery Battery thermal thermal management, management, Thermal Thermal model model of of battery battery pack, pack, Fuzzy Fuzzy logic logic control, control, Keywords: Keywords: Battery thermal management, Thermal model of battery pack, Fuzzy logic control, Battery temperature control, ANSYS. Battery temperature control,management, ANSYS. Keywords: Battery thermal Thermal model of battery pack, Fuzzy logic control, Battery temperature control, ANSYS. Battery temperature control, ANSYS. 1. INTRODUCTION ignored ignored in in the the existing existing ROMs ROMs of of battery, battery, and and the the existing existing 1. 1. INTRODUCTION INTRODUCTION ignored in not the suitable existing to ROMs of battery, and temperature the existing ROMs are be used for battery ROMs are not suitable to be used for battery temperature 1. been INTRODUCTION ignoredare in the suitable existing ROMs of battery, and temperature the existing not be used for control. Against these problems, this work the Li-ion battery battery has has extensively applied applied in in electric electric ROMs control.are Against these to problems, thisbattery work proposes proposes the Li-ion extensively ROMs not suitable to beheat usedtransfer for battery temperature Li-ion battery has tobeen been extensively applied control. Against these problems, this work proposes the ROM of battery pack whose coeﬃcient varies in electric vehicles (EVs) due high energy density and high power of battery pack whose heat transfer coeﬃcient varies vehicles (EVs) due tobeen highextensively energy density and high power ROM control. Against these problems, this work proposes the Li-ion battery has applied in electric vehicles (EVs) due to high energyThe density and high of power ROM of battery pack whose heat transfer coeﬃcient varies with the coolant ﬂow velocity, and this work changes the density (Zhang et al. (2017)). performance Liwith the coolantpack ﬂow whose velocity, and this work changes the density (Zhang et al. (2017)). The performance of LiROM of battery heat transfer coeﬃcient varies vehicles (EVs) due to high energy density and high power with the coolant ﬂow velocity, and this work changes the density (Zhang et al. by (2017)). The performance of has Li- battery temperature by controlling the coolant ﬂow velocion battery battery is aﬀected temperature. Li-ion battery battery by controlling ﬂow velocion is by Li-ion with thetemperature coolant ﬂow velocity, and the thiscoolant work changes the ◦temperature. ◦ performance density (Zhang et in al. 15 (2017)). The of has Li- battery ion battery is aﬀected aﬀected by battery has battery temperature by controlling the coolant ﬂow velocity. Furthermore, based on some the ROM is better performance C to 35 When the battery ◦temperature. ◦ C . Li-ion ity. Furthermore, based on some assumptions, assumptions, the ROM is C to 35 ◦ C . Li-ion When battery the battery better performance in 15 ◦ battery temperature by controlling the coolant ﬂow velocion battery is aﬀected by temperature. has better performance in 15 ◦ C to thermal ity. Furthermore, based on some assumptions, the ROM is simpliﬁed to obtain the maximum temperature of battery 35 C . When the battery operates at high temperature, runaway possibly ◦ operates at high temperature, thermal runaway possibly simpliﬁed to obtain the maximum temperature of battery Furthermore, based on some assumptions, the ROM is better performance in 15 accumulation. C to thermal 35 C . Therefore, When thepossibly battery ity. simpliﬁed to obtain the maximum temperature of battery pack. operates at high temperature, runaway occurs as a result of heat battery occurs as at a result of heat accumulation. Therefore, battery pack. simpliﬁed to obtain the maximum temperature of battery operates high temperature, thermal runaway possibly pack. occurs as a result of heat accumulation. Therefore, battery thermal management is to the thermal is necessary necessary to achieve achieve the optimal optimal pack. occurs asmanagement aeﬃciency result of heat accumulation. Therefore, battery Based Based the the developed developed ROM ROM of of battery battery pack, pack, this this paper paper thermal management isbattery, necessary toensure achieve theoperation optimal operation of and safe operationmanagement eﬃciency ofisbattery, andtoensure safe operation Based the developed ROM of battery pack, this in paper focuses on the temperature control of battery pack the thermal necessary achieve the optimal focuses on the temperature control of battery pack in the operation eﬃciency of battery, and ensure safe operation (Situ et al. (2017)). Based the developed ROMcontrol of battery pack, studies, this in paper (Situ et al.eﬃciency (2017)). of battery, and ensure safe operation focuses on the temperature ofprevious battery pack the air-cooling thermal management. In operation air-cooling thermal management. Inofprevious studies, the (Situ et al. (2017)). focuses on the temperature control battery pack in the air-cooling thermal management. In previous studies, air ﬂow velocity of air-cooling thermal management is set Considering the importance of battery thermal manage(Situ et al. (2017)). ﬂow velocity of air-cooling thermal management is the set Considering the importance of battery thermal manage- air air-cooling thermal management. In previous studies, the air ﬂow velocity of air-cooling thermal management is set as a constant, and thermal runaway possibly occurs when Considering the importance of battery thermal management, considerable researches and eﬀorts have been investas a constant, and thermal runaway possibly occurs when ment, considerable researches and eﬀorts have been investair ﬂow velocity of thermal air-cooling thermal management is set Considering the importance of battery thermal manageas a constant, and runaway possibly occurs when current sharply increases (He and Ma (2015)). As a result ment, considerable researches and eﬀorts have been invested to battery thermal management. The thermal model of sharplyand increases (He and Mapossibly (2015)).occurs As a result ed to battery thermal management. The thermal model of current a constant, thermal runaway when ment, considerable researches andamong eﬀorts have been invested to battery thermal management. The thermal model of as current sharply increases (He and Ma (2015)). As a result of the wide range of ambient conditions under which EVs battery is an important content these researches. of the wide range of ambient conditions under which EVs battery is an important content among these researches. current sharply increases (He and Ma (2015)). As a result ed tocomputational battery thermal management. The thermal model of of the wide range of ambient conditions under which EVs may operate, it is necessary to develop the control method battery is an important content among these researches. The ﬂuid dynamics (CFD) model has been may operate, it is necessary to develop the control method The computational ﬂuid dynamics (CFD) model has been of the wide range of ambient conditions under which EVs battery is an important content among these researches. operate, it is necessary to develop the control method to keep battery temperature in optimum under various The computational ﬂuid dynamics distribution (CFD) model has been may adopted to simulate temperature of battery, to keep battery temperature in optimum under method various adopted to simulateﬂuid temperature distribution ofhas battery, may operate, it is necessary to develop the control The computational dynamics (CFD) model been to keep battery temperature in optimum under various At PID has extensively adopted simulate temperature distribution of battery, and has been demonstrated as eﬀective to conditions. At present, present, PID control control has been been extensively and has to been demonstrated as an an eﬀective method method to conditions. keep battery temperature in optimum under various adopted to simulate temperature distribution of battery, and has been demonstrated asal. an eﬀectiveHowever, method to to conditions. At present, PID control has been extensively adopted to control system temperature. However, it design battery systems (Saw et (2016)). the adopted to At control system temperature. However, it is is design battery systems (Saw et However, the present, PID control of hasconventional been extensively and has been demonstrated asal. an(2016)). eﬀective method to conditions. adopted to control system temperature. However, it is diﬃcult to change the parameters PID design battery systems (Saw et al. (2016)). However, the CFD model with high computational cost is not suitable diﬃcult to change the parameters of conventional PID CFD model with high computational cost is not suitable adopted to control system temperature. However, it is design battery systems (Saw et al. (2016)). However, the diﬃcult to change the parameters of conventional PID control. Since operational conditions of EVs are complex CFD model with high computational cost is not suitable for real-time applications. In comparison to the CFD modSince operational conditionsofof conventional EVs are complex for real-time applications. In comparison to the CFD mod- control. diﬃcult to change the parameters PID CFD model with high computational cost is not suitable control. Since operational conditions of EVs are complex and the temperature under PID confor real-time applications. In(ROM) comparison to thereduces CFD model, the reduced-order model of battery the and changeable, changeable, the battery battery temperature under PID conel, the reduced-order model of the Since operational conditions of EVs are complex for real-time applications. In(ROM) comparison to thereduces CFD model, the reduced-order model (ROM) of battery battery reduces the control. and changeable, the battery temperature under PID control is possibly far away from optimum. In comparison target battery system to some lumped elements or states, trol changeable, is possibly far away from optimum.under In comparison target battery systemmodel to some lumped elements or states, and the battery temperature PID conel, the reduced-order (ROM) of battery reduces the trol is possibly far away from optimum. In comparison to PID control, the fuzzy logic control (FLC) with good target battery system to some lumped elements or states, enabling onboard. The ROM of Li-ion battery is developed to PID control, the fuzzy from logic control (FLC) with good enabling onboard. The to ROM of lumped Li-ion battery is developed trol is possibly far away optimum. In comparison target battery system some elements or states, to PID control, the fuzzy (FLC) with good is to used in systems enabling Theand ROM of temperatures Li-ion battery of is developed to obtain the core a robustness is suitable suitable to be belogic usedcontrol in time-varying time-varying systems to obtainonboard. the surface surface and core temperatures of a cell cell (He (He robustness PID etcontrol, the fuzzy (FLC) with good enabling onboard. The ROM of(2003)). Li-ion battery is developed robustness is suitable to belogic usedcontrol inbytime-varying systems (Tang al. (2001)). Motivated all the above, this to obtain the surface and core temperatures of athe celleﬀect (He to and Ma (2015);Park and Jaura However, (Tang et al. (2001)). to Motivated bytime-varying all the above, this and Ma (2015);Park and Jaura (2003)). However, the eﬀect robustness is suitable be used in systems to obtain the surface and core temperatures of a cell (He (Tang et al. (2001)). Motivated by all the above, this paper aims at adopting FLC to keep the battery in proper and Ma (2015);Park and Jaura (2003)). However, the eﬀect of coolant ﬂow velocity on the battery heat dissipation is paper aims at (2001)). adopting Motivated FLC to keep the battery in proper of coolant ﬂow velocity on the (2003)). battery However, heat dissipation is (Tang et al. by all the above, this and Ma (2015);Park and Jaura the eﬀect paper aims at adopting FLC to keep the battery in proper temperature. of coolant ﬂow velocity on the battery heat dissipation is ⋆ This work was supported in part by the Industrial Innovation temperature. ⋆ paper aims at adopting FLC to keep the battery in proper of coolant ﬂow velocity on the battery heat dissipation is This work was supported in part by the Industrial Innovation temperature. ⋆ Special Fundswas of Jilin Province underbyGrant 2018C035-2; in part This work supported in part the Industrial Innovation For the temperature. Special Funds of Jilin Province under Grant 2018C035-2; in part ⋆ For the rest rest of of the the paper, paper, the the ROM ROM of of battery battery pack pack whose whose work was supported in part byGrant the ofIndustrial Innovation byThis the National Nature Science Foundation China under Grant Special Funds of Jilin Province under 2018C035-2; in part For the rest of the paper, the ROM of battery packvelocity whose heat transfer coeﬃcient varies with the air ﬂow by the National Nature Science Foundation of China under Grant heat transfer coeﬃcient varies with the air ﬂow velocity Special Funds of Jilin Province under Grant 2018C035-2; in part 61520106008; andNature in part by theFoundation Scientiﬁc and Technological Deby the National Science of China under Grant For the rest ofcoeﬃcient theSection paper,varies the ROM ofthe battery packvelocity whose 61520106008; and in part by the Scientiﬁc and Technological Deheat transfer with air ﬂow is developed in 2. The ROM of battery pack by the National Science of China China under Grant is developed in Section varies 2. The ROM of battery pack velopment Plan Project inbyJilin Province under 61520106008; andNature in part theFoundation Scientiﬁc of and Technological Deheat transfer coeﬃcient with the air ﬂow velocity velopment Plan Project in Jilin Province of China under Grant is developed in Section 2. The ROM of battery pack validated in Section 3. The FLC for battery thermal 61520106008; and in part by the Scientiﬁc and Technological De20170520060JH. is validated in Section 3. The FLC for battery thermal velopment Plan Project in Jilin Province of China under Grant is developed in Section 2. The ROM of battery pack 20170520060JH. is validated in Section 3. The FLC for battery thermal velopment Plan Project in Jilin Province of China under Grant 20170520060JH. is validated in Section 3. The FLC for battery thermal 20170520060JH.

2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 285 Copyright 2018 IFAC 285 Control. Peer review© under responsibility of International Federation of Automatic Copyright © 2018 IFAC 285 10.1016/j.ifacol.2018.10.047 Copyright © 2018 IFAC 285

IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018Xiaojing Gao et al. / IFAC PapersOnLine 51-31 (2018) 262–267

management is designed in Section 4. Compared with PID control, the eﬀectiveness of FLC is validated with the ANSYS and MATLAB co-simulation in Section 5. Section 6 summarizes this paper.

263

2. DEVELOPMENT OF REDUCED-ORDER MODEL In this section, the ROM of a cell is ﬁrst developed. Based on the ROM of a cell, the ROM of a battery pack is developed to obtain the temperature range of battery pack.

Assuming there is a uniform temperature in a cell, the ROM of a cell is developed. Based on the energy balance, energy accumulated in the cell Qaccumulation,i is expressed as dTb,i = Qgenerated,i − Qdissipated,i . Qaccumulation,i = cb mb dt (1) where cb denotes the speciﬁc heat capacity of a cell. mb represents the mass of a cell. Tb,i is the temperature of a cell. Qgenerated,i is heat generation inside a cell. i is the index number of a cell. Qdissipated,i represents the surface convection heat transfer. According to Bernardi formula (Newman et al. (1985)), the mixing heat and phase-change heat terms are mostly ignored, and Qgenerated,i is dEoc dEoc Qgenerated,i = I(Eoc − E) − ITb,i = I 2 R − ITb,i . dTb,i dTb,i (2) where I is charging current. The direction of charging current is deﬁned as positive. E represents the terminal voltage of a cell. Eoc denotes the open circuit voltage of a cell. dEoc /dTb,i denotes the reversible entropic loss. dEoc /dTb,i written as a1 is taken as a constant in this work. R represents the internal resistance of a cell. R is approximated as a function of temperature due to the weak dependence on SOC. R is R = −0.00016Tb,i + 0.0583. (3) According to the equation (2)-(3), the heat generation of a cell Qgenerated,i is Qgenerated,i = (−a1 I − 0.00016I 2 )Tb,i + 0.0583I 2 . (4) According to Newton’s law of cooling, the surface convection heat transfer Qdissipated,i is expressed as (5) Qdissipated,i = hAb (Tb,i − Ta,i ). where Ab denotes the heat radiation area of a cell. Ta,i is the air ﬂow temperature near a cell. h denotes the heat transfer coeﬃcient. Considering the eﬀect of wind velocity on the battery heat dissipation, h is expressed as a function of wind velocity v. h is N u · ka . (6) h= D where ka is the thermal conductivity of air. D denotes the diameter of a cell. N u represents the Nusselt number. The N u number is correlated to Reynolds number (Re) (Mahamud and Park (2011)). The N u number is −0.25 0.4 0.61 100 < Re < 102 0.8Re 0.5P r 0.61P rw −0.25 2 3 0.51Re

Pr P rw 10 < Re < 10 P r0.61 P rw −0.25 103 < Re < 2 × 105 0.021Re0.84 P r 0.65 P rw −0.25 2 × 105 < Re < 2 × 106 (7)

0.27Re

Fig. 1. Battery system in in-line cell arrangement L v. (8) L−D ρa vmax D . (9) Re = µ where P r denotes the Prandtl number of air ﬂow in the entrance. P rw represents the Prandtl number of air ﬂow near the wall of cells. µ represents the air viscosity. vmax is the maximum air ﬂow velocity in the transverse spacing (L − D) between two vertically adjacent cells. ρa denotes the air density. v denotes the free space velocity. L is the distance between the two adjacent cell centers. The battery submodule considered in this work is shown in Fig. 1. vmax =

2.1 Development of Reduced-order Model of a Cell

Nu =

0.63

286

Considering cooling eﬀectiveness and cost, the wind velocity in the range of 0.5m/s − 10m/s is considered in this work, and the range of Re number is 3264.8-65295. The N u number is expressed as N u = 0.27Re0.63 P r0.61 P rw −0.25 . (10) According to the equation (6)-(10), h is ( )0.63 ( )0.25 0.27ka P r0.36 ρa DLv Pr h= . (11) D µ (L − D) P rw where D , L , ρa , µ, P r , P rw , and ka are set as constants, as shown in Table 1. h is a function of wind velocity v . Let

( )0.63 ( )0.25 ρa DL Pr 0.27ka P r0.36 . (12) D µ (L − D) P rw According to the equation (5), (11), and (12), Qdissipated,i is Qdissipated,i = a2 Ab (Tb,i − Ta,i )v 0.63 . (13) According to the equation (1), (4), and (13), the temperature of a cell Tb,i (i = 1, 2, · · · 6) is expressed as [ ] (−a1 I − 0.00016I 2 ) − a2 v 0.63 Ab ˙ Tb,i = Tb,i c b mb (14) 2 0.63 Ab Ta,i 0.0583I + a2 v + . c b mb where Ta,i (i = 1, 2, · · · 6) is the air ﬂow temperature near a cell. a2 =

From the equation (14), Ta,i needs to be measured to obtain Tb,i . Ta,1 is roughly equal to the ambient temperature Ta in this work. Ta,i (i = 2, · · · 6) is hard to be measured in actual system. To obtain Tb,i , it needs some methods to calculate Ta,i instead of directly measuring Ta,i . In (Li et al. (2013)), temperature non-uniformity among diﬀerent cells in the battery pack is investigated by CFD model. The simulation results show that the temperatures of cells and air ﬂow near cells in the streamwise direction are generally increasing. The lowest cell temperature occurs in the rows that are nearest to the inlet, and the highest cell temperature occurs in the rows that are

IFAC E-CoSM 2018 264 Changchun, China, September 20-22, 2018Xiaojing Gao et al. / IFAC PapersOnLine 51-31 (2018) 262–267

nearest to the outlet. This work makes assumptions that the temperatures of cells and air ﬂow near cells in the streamwise direction are approximately increasing in equal size. Based the assumptions, Ta,i can be calculated, and the temperature range of battery pack is obtained, without measuring Ta,i . 2.2 Development of Reduced-order Model of a Battery Pack Based on the assumptions in Section 2.1, it only needs to obtain the temperatures of the ﬁrst cell and the sixth cell to predict the temperature range of battery pack. According to the equation (14), the thermal model of the ﬁrst cell is expressed as [ ] 2 0.63 (−a I − 0.00016I ) − a v A 1 2 b T˙b,1 = Tb,1 c b mb (15) 0.0583I 2 + a2 v 0.63 Ab Ta,1 + . c b mb The energy conservation law for air ﬂow over battery pack is Qt1 = Qt2 . (16) where Qt1 denotes heat absorbed by air ﬂow from the battery system inlet to outlet. Qt2 represents the total amount of heat that the battery pack releases to air ﬂow. Qt1 and Qt2 are written as Qt1 = ρa ca Sa v(Ta,6 − Ta,1 ). (17) Qt2 = Qdissipated,6 + . . . + Qdissipated,6 = a2 v 0.63 Ab [(Tb,1 − Ta,1 ) + · · · + (Tb,6 − Ta,6 )] . (18) where Sa denotes the ventilation area at the entrance.

Assuming the temperatures of cells and air ﬂow near cells in the streamwise direction are roughly increasing in equal size, Ta,i and Tb,i are written as 1 Tb,2 = Tb,1 + (Tb,6 − Tb,1 ) 6−1 .. (19) . 6 − 2 Tb,5 = Tb,1 + (Tb,6 − Tb,1 ). 6−1 1 (Ta,6 − Ta,1 ) Ta,2 = Ta,1 + 6 − 1 .. (20) . 6−2 Ta,5 = Ta,1 + (Ta,6 − Ta,1 ). 6−1 Taking the equation (17)-(20) into the equation (16), Ta,6 is 3a2 Ab (Tb,1 + Tb,6 ) Ta,6 = ρa ca Sa v 0.37 + 3a2 Ab (21) ρa ca Sa v 0.37 − 3a2 Ab T . + a,1 ρa ca Sa v 0.37 + 3a2 Ab Taking the equation (21) into the equation (13), Qdissipated,6 is written as ρa ca Sa a2 Ab v Tb,6 − ρa ca Sa v 0.37 + 3a2 Ab 2 2 0.63 3a2 Ab v ρa ca Sa a2 Ab v − 3a22 A2b v 0.63 Tb,1 − Ta,1 . 0.37 ρ a c a Sa v + 3a2 Ab ρa ca Sa v 0.37 + 3a2 Ab (22) Qdissipated,6 =

287

Taking the equation (4) and (22) into the equation (1), the thermal model of the sixth cell is expressed as f1 (v) (−a1 I − 0.00016I 2 ) − f2 (v) Tb,1 + Tb,6 T˙b,6 = c b mb c b mb 2 0.0583I + f3 (v)Ta,1 + . c b mb (23) where 3a22 A2b v 0.63 f1 (v) = ρa ca Sa v 0.37 + 3a2 Ab ρa ca Sa a2 Ab v f2 (v) = (24) ρa ca Sa v 0.37 + 3a2 Ab ρa ca Sa a2 Ab v − 3a22 A2b v 0.63 f3 (v) = . ρa ca Sa v 0.37 + 3a2 Ab The ROM of the battery pack are described by the equation (15) and (23). Initializing current I, wind velocity v, and ambient temperature Ta,1 , the temperatures of the ﬁrst cell and the sixth cell are calculated by the equation (15) and (23), without measuring Ta,i (i = 2, · · · 6). From equation (15) and (23), the temperatures of cells are related to v, and the temperatures of cells are changed by controlled v. 3. VALIDATION OF REDUCED-ORDER MODEL After the ROM of battery pack is developed, the accuracy of ROM needs to be validated. As a result of the complexity of building a test platform, a CFD model validated with the experimental results of in-line tube-bank systems is developed to validate the ROM of battery pack. 3.1 CFD Model Development and Validation A CFD model is developed in ANSYS/FLUENT 14.0. Fig.1 provides a schematic of battery system considered for this work. The coolant air ﬂow enters from the left, and exits from the right. The cylindrical Li-ion battery (A123 LiFePO4, capacity: 2.3Ah, D × Height = 26mm × 65mm) is research target that this work considers. The transverse piZhao:2015tch ( W ) and longitudinal pitch (L ) are both set as 53mm. This work brieﬂy describes the development of CFD model. More information about the CFD model is provided in (Ru. (2017)). A solid zone and ﬂuid zone meshed in uniform quadrilateral is adopted to model cells and air ﬂow. A user deﬁned function (UDF) is adopted to model heat release rate as a function of cell temperature. Reynolds stress and renormalization group turbulent model ( k − ε) is adopted to enhance wall treatment. The cell heat generation Qgenerated ,i is calculated by equation (4). After the CFD model is developed, the accuracy of the CFD model needs to be veriﬁed. The battery arrangement considered in this work is approximated as a in-line tubebank system. To verify the accuracy of CFD model, the correlation between N u number and Re number simulated by CFD model is compared with the empirical correlation summarized by Zukauskas and Ulinkskas (expressed in the equation ((7)-(9)). The N u number using the results of the CFD simulation is calculated by a log-mean temperature diﬀerence ( TLM T D ), and is given by the equation (25)(28). These parameters used in the correlation are shown in Table 1.

IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018Xiaojing Gao et al. / IFAC PapersOnLine 51-31 (2018) 262–267

˄˅

265

Fig. 2. Comparison of N u number correlation between the CFD simulation result and the empirical correlation

Air (properties / ) ρa kg m3 ca (J/kgK) ka (W /mK) µ (kg/ms) Pr P rw

˄ć˅

Value 0.005309 0.073 1120.97 -0.0003 0.053 0.002275

Value 1.185 1005 0.0263 0.00001835 0.702 0.7

˄˅

Fig. 3. Current proﬁle of US06 condition

Table 1. Parameters and thermophysical properties used in this work Battery (properties ) Ab m 2 mb (kg) cb (J/kgK ) a1 (V /K) L((m) ) Sa m 2

˄˅

Fig. 4. ROM validation results under v = 2.5m/s

h·D Nu = . (25) ka Ma ca (Ta,6 − Ta,1 ) h= . (26) 6πDHTLM T D (27) Ma = v · Sa . (Tb,6 − Ta,6 ) − (Tb,1 − Ta,1 ) . (28) TLM T D = ln((Tb,6 − Ta,6 )/(Tb,1 − Ta,1 )) where Ta,1 is the temperature approximation of air ﬂow at the inlet of battery system. Ta,6 is the temperature approximation of air ﬂow at the outlet of battery system. Ma represents the mass ﬂow rate. ca is the air heat capacity. H denotes the length of a cell. Sa represents the ventilation area. The comparison of N u number correlation between the CFD simulation result and the empirical correlation summarized by Zukauskas and Ulinkskas is shown in Fig. 2. From Fig.2, the N u number correlation from the ROM and the CFD model are well matched. Therefore, it is reasonable to replace real experimental values with the CFD simulation results in this work.

˄ć˅

˄˅

Fig. 5. ROM validation results under v = 5.0m/s From Fig.4, when v is set as 2.5m/s, the maximum temperature rise of the sixth cell is 5.3◦ C. From Fig.5, when v is set as 5.0m/s, the maximum temperature rise of the sixth cell is 3.9◦ C. Obviously, the cooling eﬀect of air ﬂow under v = 5.0m/s is better than v = 2.5m/s. When EVs operate at diﬀerent conditions, control strategy is necessary to improve the cooling performance and reduce coolant air ﬂow consumption. 4. DESIGN OF FUZZY LOGIC CONTROL

3.2 Reduced-order Model of a Battery Pack Validation Initializing temperatures of cells, current and wind velocity, the temperature range of battery pack is calculated by the equation (15) and (23) in MATLAB. Compared with CFD simulation results, the accuracy of ROM is validated. The initial temperatures of air ﬂow and cells are both set as 25◦ C. The air ﬂow velocity is set as 2.5m/s and 5.0m/s, respectively. The simulations are taken under High Speed Transient Control Cycle (US06) condition, and the current proﬁle of US06 condition is shown in Fig. 3. The comparisons of battery temperature between CFD simulation and ROM of battery pack are shown in Fig. 4 and Fig. 5. The results show that the battery temperature from the ROM are good agreement with the CFD simulations, and the model errors are maintained within 0.5◦ C. Therefore, the ROM of a battery pack is accurate to be used to predict battery pack temperature. 288

Considering nonlinearity and time-varying characteristics exist in the ROM of the battery pack, the FLC is developed to control the temperature battery pack in this work. The FLC consists of fuzziﬁer, inference engine, rule base, and defuzziﬁer, as shown in Fig. 6 (Revathi and Sivakumaran (2016)). Firstly, the input is converted to fuzzy values by fuzziﬁer. Then, the fuzzy values are sent to the inference engine and processed with fuzzy rules. Finally, defuzziﬁer transforms the union of fuzzy sets into exact values. The inputs of FLC are the temperature error e and the change of temperature error ∆e, and e and ∆e are expressed as e = Tb,6 − Tt arg et . (29)

∆e = e(t + 1) − e(t). (30) where Tb,t arg et is the target temperature of battery. e(t) is the temperature error at time t.

IFAC E-CoSM 2018 266 Changchun, China, September 20-22, 2018Xiaojing Gao et al. / IFAC PapersOnLine 51-31 (2018) 262–267

3) When e is relatively small, ∆e is relatively large, relatively small wind velocity v is used to cool battery. The FLC including 12 rules is used to control battery temperature, and the rule of FLC is listed in Table 2. The fuzzy inference engine transforms the fuzzy rule base into a fuzzy linguistic output. Centroid membership function is used for defuzziﬁcation process to obtain the output v. The centroid membership function is expressed in equation (30). ∫ zg(z)dz v= . (31) g(z)dz where g(z) denotes the fuzzy rules.

Fig. 6. Block diagram of the FLC

Table 2. Rules of FLC

v

∆e

S M L

VS VS S S

S S S M

e M M M L

L M L L

5. SIMULATION RESULTS AND DISCUSSION

ANSYS and MATLAB co-simulation is adopted to validate the eﬀectiveness of FLC. The ﬂowchart of cosimulation is illustrated in Fig. 8. The simulations are taken under New European Driving Cycle (NEDC) condition, and the current proﬁle of NEDC condition is shown in Fig. 9. First, the wind velocity v is calculated by FLC in MATLAB. The v is transferred to ANSYS. Then, the temperature variation of battery pack is simulated in ANSYS under the v. Finally, the temperature data of battery pack is collected in ANSYS by UDF, and the temperature data is transferred back to MATLAB to obtain v at next time.

Fig. 7. (a) Membership function for e; (b) Membership function for ∆e; (c) Membership function for wind velocity v The wind velocity v is the output of FLC. Considering the cooling eﬃciency and cost, the wind velocity in the range of 0.5m/s − 10m/s is considered in this paper. The range of temperature error e is set as -5 to 10 in this work. The range of ∆e is set as -15 to 15. Then the input and output are divided into fuzzy subsections and expressed by linguistic variable. The fuzzy variable of e is divided into L (large), M (medium), S (small), and VS (small). The fuzzy variable of ∆e is divided into L (large), M (medium), and S (small). The fuzzy variable of v is divided into L (large), M (medium), S (small), and VS (very small). The triangular fuzzy membership function is chosen, as shown in Fig. 7. These rules of FLC are based on the knowledge and practical experience of cooling requirement of battery thermal management.

To validate the eﬀectiveness of FLC, the simulations are performed under three conditions for comparison. The ﬁrst condition is that the wind velocity is ﬁxed at v = 2.5m/s. The second condition is that PID control is applied to control battery pack temperature. The third condition is that FLC is used to control battery pack temperature. The initial temperatures of cells are set as 38◦ C. The temperature of coolant air ﬂow is set as 32◦ C. The control output named the maximum temperature control target is set as 35◦ C. When the wind velocity is ﬁxed at v = 2.5m/s, the simulation result is shown in Fig. 10. The sixth cell temperature reaches the target temperature at 200s. The cooling eﬃciency of air ﬂow is slow, and thermal runaway possibly occurs when the current dramatically increases. During t = 200s − 1180s, as a result of cooling fast, the sixth cell temperature is lower than the target temperature, and the

1) When e and ∆e are relatively large or small, large or small wind velocity v is used to cool battery. 2) When e is relatively large and ∆e is relatively small, relatively large wind velocity v should be used to cool battery. 289

Fig. 8. Scheme of co-simulation

IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018Xiaojing Gao et al. / IFAC PapersOnLine 51-31 (2018) 262–267

varies with the wind velocity is ﬁrst developed to monitor the battery temperature. A CFD model validated with the experimental results of in-line tube-bank systems is developed to validate the accuracy of ROM. The FLC is then developed to change the temperature of battery pack by controlling wind velocity. Finally, ANSYS and MATLAB co-simulation is adopted to validate the eﬀectiveness of FLC under NEDC condition. The simulation results show that the FLC has a faster, more accurate, and more stable control performance compared with the PID controller. An experimental demonstration of the control strategies developed in this work is undergoing.

˄˅

˄˅

Fig. 9. Current proﬁle of NEDC condition ˄ć˅

REFERENCES

˄˅

Fig. 10. Temperatures of the ﬁrst cell and the sixth cell under v = 2.5m/s

˄ć˅

˄˅

267

Fig. 11. Temperatures of cells under PID control and FLC coolant air ﬂow is wasted. The sixth cell temperature can not stabilize around the target temperature. It needs a control algorithm to control temperature in target value and reduces air ﬂow consumption. The temperature variations of the ﬁrst cell and the sixth cell employing PID control and FLC are shown in Fig. 11. The sixth cell temperature employing PID control and FLC reaches the target temperature at 140s and 80s, separately. Obviously, compared with the PID control, the cooling rate under FLC is improved greatly. From Fig. 11, the maximum control error of FLC is about 0.2 ◦ C, and the maximum control error of PID control is 0.8 ◦ C. In comparison to PID control, the temperature ﬂuctuation of the sixth cell employing FLC is smaller. The FLC quickly and precisely controls battery temperature at the target value. Under PID control, the temperatures of cells are possibly far away from the target value when working condition varies dramatically. In comparison to PID control, FLC achieves a faster, more accurate, and more stable thermal management. 6. CONCLUSION In summary, this work develops the ROM of a battery pack and investigates the thermal management employing FLC. The ROM of a battery pack whose heat transfer coeﬃcient 290

He, F. and Ma, L. (2015). Thermal management of batteries employing active temperature control and reciprocating cooling ﬂow. International Journal of Heat and Mass Transfer, 83, 164–172. Li, X., He, F., and Ma, L. (2013). Thermal management of cylindrical batteries investigated using wind tunnel testing and computational ﬂuid dynamics simulation. Journal of Power Sources, 238, 395–402. Mahamud, R. and Park, C. (2011). Reciprocating air ﬂow for li-ion battery thermal management to improve temperature uniformity. Journal of Power Sources, 196, 5685–5696. Newman, Bernardi, and Pawlikowski (1985). A general energy-balance for battery systems. Journal of the Electrochemical Society, 132, 5–12. Park, C. and Jaura, A.K. (2003). Dynamic thermal model of li-ion battery for predictive behavior in hybrid and fuel cell vehicles. Sae Transactions, 112, 1835–1842. Revathi, S. and Sivakumaran, N. (2016). Fuzzy based temperature control of greenhouse. Ifac Papersonline, 49, 549–554. Saw, L.H., Ye, Y., Tay, A.A.O., Wen, T.C., Seng, H.K., and Ming, C.Y. (2016). Computational ﬂuid dynamic and thermal analysis of lithium-ion battery pack with air cooling. Applied Energy, 177, 783–792. Situ, W., Zhang, G., Li, X., Yang, X., Wei, C., Rao, M., Wang, Z., Wang, C., and Wu, W. (2017). A thermal management system for rectangular lifepo4 battery module using novel double copper mesh-enhanced phase change material plates. Energy, 141, 613–623. Tang, K.S., Man, K.F., Chen, G., and Kwong, S. (2001). An optimal fuzzy pid controller. IEEE Transactions on Industrial Electronics, 48, 757–765. Zhang, Y., Xiong, R., He, H., and Shen, W. (2017). Lithium-ion battery pack state of charge and state of energy estimation algorithms using a hardware-in-theloop validation. IEEE Transactions on Power Electronics, 32, 4421–4431. Ru, J.(2017). A Study on Thermal Model and Temperature Control of an Air-cooled Battery Pack for Electric Vehicles. Jilin University.